HOLA: a High-Order Lie Advection of Discrete Differential Forms With Applications in Fluid Dynamics

Author: McKenzie, Alexander George

Year: 2007

Degree: Master's thesis

Advisor: Desbrun, Mathieu

Committee Member: Unknown, Unknown

Option: Computer Science

DOI: 10.7907/0TJH-M778

Abstract

The Lie derivative, and Exterior Calculus in general, is ubiquitous in the elegant geometric interpretation of many dynamical systems. We extend recent trends towards a Discrete Exterior Calculus by introducing a discrete framework for the Lie derivative defined on differential forms, including a WENO based numerical scheme for its implementation. The usefulness of this operator is demonstrated through the advection of scalar and vector valued fields (arbitrary discrete k-forms) in a desirable intrinsic and metric independent fashion. Examples include Lie advection of fluid flow vorticity, and we conclude with a significant discussion on the conservative Lie advection of fluid mass density for robust free surface flows in computer graphics.

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